We propose a definition of branching-type stationary stochastic processes on rooted trees and related definitions hyper-positivity for functions the unit circle set non-negative integers. then obtain (1) necessary sufficient condition tree existence non-trivial it, (2) complete criterion hyper-positive in setting homogeneous terms variant classical Herglotz-Bochner Theorem, (3) prediction theor...

Many natural phenomena exhibit a stochastic nature that one attempts at modelling by using processes of different types. In this context, often is interested in investigating the memory properties phenomenon hand. This usually accomplished computing autocorrelation function numerical series describing considered phenomenon. Often, especially when considering real world data, must be computed st...

The use of spectral analysis techniques for the study of stochastic processes that occur over multidimensional spaces, such as ocean wind-waves or ocean bottom roughness, leads to a large number of possible spectral quantities one can use in a description of the process. The multidimensional case presents difficulties since this variety does not arise in the study of processes that depend on on...

We propose a test of the hypothesis of stochastic monotonicity. This hypothesis is of interest in many applications in economics. Our test is based on the supremum of a rescaled U-statistic. We show that its asymptotic distribution is Gumbel. The proof is difficult because the approximating Gaussian stochastic process contains both a stationary and a nonstationary part and so we have to extend ...

Let 0¡ 62 and let T ⊆R. Let {X (t); t ∈ T} be a linear fractional -stable (0¡ 62) motion with scaling index H (0¡H ¡ 1) and with symmetric -stable random measure. Suppose that is a bounded real function with compact support [a; b] and at least one null moment. Let the sequence of the discrete wavelet coe cients of the process X be { Dj;k = ∫ R X (t) j;k(t) dt; j; k ∈ Z } : We use a stochastic i...

Suppose that there are k ≥ 2 different systems (i.e., stochastic processes), where each system has an unknown steady-state mean performance and unknown asymptotic variance. We allow for the asymptotic variances to be unequal and for the distributions of the k systems to be different. We consider the problem of running independent, single-stage simulations to make multiple comparisons of the ste...

We explain why an assumption of stationarity is suucient to give us the ability to detect aliasing in a temporally sampled signal process. We then deene a notion of stationarity that makes sense for single waveforms. (This is done without assuming that the waveform is a sample path of some underlying stochastic process.) We show how to use this concept to detect aliasing in sampled waveforms. T...

Torque fluctuations due to magnetorotational turbulence in proto-planetary disks may greatly influence the migration patterns and survival probabilities of nascent planets. Provided that the turbulence is a stationary stochastic process with finite amplitude and correlation time, the resulting diffusive migration can be described with a FokkerPlanck equation, which we reduce to an advection-dif...

SUMMARY. For a stationary *-mixing stochastic process, the law of iterated logarithm, asymptotic normality and weak convergence to Brownian motion processes

Geometric characteristics of random surfaces play a crucial role in areas such as geoscience, environmetrics, astrophysics, and medical imaging, just to mention a few examples. Numerous real data have been modelled as Gaussian random processes or fields and studying of their excursion sets is now a well developed subject. Sojourn measures provide a classical approach to addressing various appli...